I can say that I've seen a number of cases of high-ability underachievers who turned themselves around and led highly productive, enriching lives, and those turnarounds began in early adulthood. So in my experience, 11 is definitely not to young.

I met these guys while in the Navy. I worked in a highly-technical field, in which two years' worth of college electronics is compressed into 36 weeks, testing is every week, 75% is the cut-off for failure, there were significant deterrents to failure (nighttime remediation, held back in school longer, eventually kicked out to join the fleet in a paint-chipping role), and significant motivation to compete for excellence (ranking by class averages, first in line to choose next duty station).

Needless to say, this environment sorts out much of the chaff. Within this group I found a subgroup of young men who were clearly my peers... similar in interests, abilities, etc. I just assumed that they breezed through K-12 with as little effort as necessary to stay on the honor role, as I did, but much of the high-ability group had instead breezed by with as little effort as necessary to avoid repeating a grade. They cut 15-20 classes a quarter, didn't do homework, or copied from a friend, etc.

One of the guys had appeared one time too many in front of the judge on minor issues, and when he got accidentally swept up in the search for the perp of a big one, he was given the option of joining any military branch that would get him out of the state, or going to jail. Today, he is running the QA department of a manufacturer of extremely sensitive commercial aircraft equipment.

It would be easy to associate the turnaround with the authoritative nature of the military. But it would be dead wrong. One trait these guys all shared was a disregard for authority. Anyone who tried shouting an order at these guys would find themselves regretting it sooner or later. That wasn't something generally done in the technical fields anyway, because when you need talented people, you have to treat them a certain way to get them to do their best. There was a whole different culture in the electronics shops than, say, the engine room. But if an engineering officer found himself in charge of a detail with one of these guys, and started shouting orders, these guys would respond with passive resistance, then later create a situation in which the engineering officer made himself look really, really bad.

Based on this experience, I'd advise that anyone who is currently dealing with a child 11 or older that has tuned out the authority of the teachers to strongly reconsider adopting an authoritative approach as a possible solution. The child is already against what seems to be commands to perform useless and pointless tasks. If you start adding your voice to that of the teachers, you're only making yourself part of their problem.

So... what really turned these guys' lives around?

The work.

The work was interesting, challenging, and important. People's lives and millions of dollars depended on the state of the equipment, and how they performed their jobs to maintain it. These same guys who wouldn't invest five minutes to iron a uniform shirt would work 36 hours straight to resolve an equipment problem, and good luck pulling them away to get some sleep. Offer to call in civilian technical resources to assist, though, and you'll get yelled at. They took genuine pride in their abilities and their roles.

So... how do you relate this to an 11yo tuning out in school, so he can turn things around well before the onset of adulthood has limited his options? Here's how I'd do it:

1) Fight for proper placement in a challenging educational environment.
2) Set clear guidelines on what are acceptable minimum limits of effort, tailored to the individual strengths and weaknesses of that child. A child will be burned out if they're expected to do their very best on every task, no exceptions. Let them have some room to breathe.
3) Give them some guidance on how something that may seem meaningless to them now can build to something meaningful later. This is critical to getting "buy in."
4) Create positive rewards in which the child can gain access to more of what they love if they invest more in doing the things they don't.
5) Create negative rewards in which the child loses some access to the things they love if they fail to maintain minimum standards.