You've already got a third of your stack invested in the hand. I think your opponent's range is much wider than you've given him credit for, especially at the 11s. He's invested most of his chips and you now you are getting great pot odds given the fact that you have an overpair. Minraises usually indicate a huge hand, especially over your pot sized bet, but the fact that a minraise almost puts him all in makes me think you should just shove the rest of your chips in. I think you're ahead often enough here to make folding a huge mistake.