First, welcome to the Forum!
THERE IS NO WAY A REASONABLY EQUIPPED ? TON TRUCK CAN HANDLE AN 11,000# FW!!
The dry wt is useless. The FW probably weighed more than that when you brought it home. Nobody goes camping in an empty trailer. Use the FW GVWR, or dry wt + CCC, or 10,500#. The REAL pin wt will be about 20% of this weight, or 2100#. The published hitch wt is about 20% of the dry wt.
The tow vehicle will need sufficient payload to handle: FW pin wt of 2100#, Weight of FW hitch of about 200#, Weight of all passengers, pets, tools, cargo and firewood. I will guess 500#, but use YOUR weight! This totals 2800# MINIMUM payload.
I am not aware of any ? ton pickup built from 2010 to 2014 with that much payload.
Every vehicle built since 2009 has a yellow label on the driver door B pillar that states the max weight of all passengers and cargo shall not exceed XXXX lbs. This is the max payload of the vehicle, including all options and a full tank of fuel based on its weight when it left the factory.
Look at this label on any potential tow vehicles to make sure it is up to the task, and do not let some uninformed salesman try to change your mind. This 2800# may exceed the payload on some well equipped ? ton trucks, so please look!
You may wish to consider a 1 ton truck. For a SRW 1 ton, the dimensions are almost identical to their ? ton cousin. The price is nearly identical for used models. The 1 ton comes with a heftier suspension and a GVWR of 11,500# (for most) compared to 10,000# or 9900# for most ? ton trucks. This adds about 1000# more payload on average for the 1 ton version.
Nobody EVER complained about too much truck!