11+ may be a tall order depending on the soil.
REGARDLESS OF DETECTOR, If depth is all you are worried about just make sure you get a detector with ground balance, get the big coil, and if you think or know you have poor soil make sure that coil is a DD.
Tejon, Vaquero, Fisher 1266, F4, F5, F70, T-2, are the first that come to mind that you can get either new or at least used in that price range and are most likely to go that deep (sensitive with ground balance). Out of those, the F4 and Teknetics T-2 comes stock with the deepest seeking coil. The others might manage the depth with their slightly smaller non-DD stock coil (again, it depends on your soil conditions).