At that age an occasional early bedtime is the best, rather than moving it all earlier for multiple nights.
11 hours would be about normal at 6yo, but I had a friend whose children did closer to 13.
I'd definitely get her to bed at a point 11 hours from when you need wakeup and work from there. Maybe every few nights you need an earlier night, but consistency is the key.
Also if she's always super tired it would be worth getting her checked out. A boy near us (6 at the time) had sleep apnea and while he slept 12+ hours he was always super tired, until they sorted that out and he was a different child.