It is amazing how the mind of an 11-year-old works! I have an 11-year-old daughter, so I understand! My daughter has to read each night before she goes to bed. It helps her get sleepy and has become her routine (habit). Of course, we are happy with that habit! (Our children do not have TVs in their rooms).
Try suggesting that your son read, draw or journal before going to bed--something different. However, I know a lot of people (children and adults) that have to watch a little TV in bed before they go to sleep. It is like a nightly ritual.
Have you seen your son have bad dreams when he doesn't watch TV before bedtime? Chances are TV is his bedtime ritual that he is comfortable with. If he does well with his school work, plays well during the day, and does not lose privileges with bad behavior, I would let him watch his movie each night. However, place limits on how long he can watch and what he watches.