I just left a dealer. First thing I look at after the motor, is the Rear Gear. Higher than a 3.55, no need to look any farther.
Actually, in truth. It would be best just to go into the office, and tell them what you want, then let them find it for you. Because the chance you will find a F150 on a dealer lot rated to tow 11,000lbs, Is slim to none.
The only F150s that will tow 11,000 are the EcoBoost, with either a 3.73, or a 4.10, and 6.2L V8, with a 3.73 rear, and very few if any dealers order that combination. Plus they of course have to have the higher GVWR. so you may as well get them to find you one with out wasting your time on the lot.