The only way you can get a 11k+ tow rating in a F150 is with the HD Payload package. That bumps the payload rating to over 2k. Payload rating is the biggest limiting factor when the tow rating is determined.

Factors in determining max tow rating:

GVWR - gross vehicle weight rating
GAWR (front/rear) - gross axle weight rating
Payload rating - GVWR minus the weight of the truck
GCWR - gross combined weight rating (truck plus trailer)

Trailer tongue weight should be between 8 and 15 % of the trailer gross weight, 12 % is ideal.. The tongue weight is considered payload.

If you want to check everything out, load up the truck with what will be in it - passengers and cargo - for your trip. Connect the trailer, also loaded for the trip, and go visit a CAT scale at a truck stop. Run it over the scales and get the weight of each axle, truck and trailer. Then drop the trailer and run over the scales again, getting axle weights. If you are an engineer, I think you can do the math to see exactly where you stand. This will tell you the tongue weight, axle weights, and gross weights. It should cost you $15.50 for a weigh and 1 reweigh.

 

Funny you should say that, I was must mapping the closest CAT scales for my trip home w/ the empty trailer to see where I'm starting off from