After going through the headache of checking which truck could pull what, I created a online calculator to help determine if the trailer is within the truck's capacities. Here's a link:
Trailer Towing Calculator
2013 Ford F150 towing capacities
I punched in the following numbers, but please check because only you know the exact specs of your truck.
For the truck...
Curb Weight: 5586
Maximum Loaded Trailer Weight: 11300 (could be smaller if you have 4wd)
Gross Vehicle Weight Rating: 8200 (assuming you have HD payload package)
Gross Combined Weight Rating: 17000
Passenger Weight: 400
Additional Weight: 0
For the trailer...
Unloaded Weight: 7623
Unloaded Hitch Weight: 1145
15% GVWR on hitch
Based on the numbers above, you can technically pull it but you're really close to being over the limit on the combined weight.