The rating that will bite you first, is payload. You will run out of that, before you get close to your tow capacity rating. Manufacturers tow capacities are based on a stripped down truck model, with a lone driver, and no cargo. Everything and everybody you put in or on the truck, takes away from that capacity number.
You know your GVW (6400). Take the truck to a scale and get it's actual weight. Subtract the actual weight from 6400 lbs. The left over is your payload.
Payload is your capacity to carry the weight of passengers, cargo (in the truck), and tongue weight from the trailer. From your payload number, subtract weight of your occupants and truck cargo. What's left over, is available for trailer weight.
Average hitch weight is about 12 percent of loaded trailer weight.
Average trailer load (dishes, pots and pans, camp chairs, BBQ, bedding, groceries, water, etc) is about 800 - 1000 lbs.
Using average numbers, your trailer's loaded weight will be in the area of 73 - 7500 lbs and hitch weight will be over 900 lbs. The weight distribution hitch will add another 80 - 100 lbs.
It's difficult for us to say "yes" or "no" about your towing saftey, we don't know what your payload or occupant / cargo weight requirements are.
Example:
If you have 1200 lbs payload, 500 lbs occupants, and put a 700 lb four wheeler in the bed of the truck, you don't have payload left to tow anything.