Should be doable
Open drivers door and see what Cargo Carrying Capacity (Payload) rating is ...~1500# or so????
That is number you subtract your weight above 150#, all occupants weight, all stuff in truck cab (door pockets, seat pockets, console, in floor/under seats, in bags/back packs etc), anything in truck bed, weight of hitch shank/ball.
What is left over is amount of tongue weight you can carry.
6000# trailer.....12% for tongue weight-----720# (almost half of that 1500# payload)
So add up the cumulative weights and then subtract from the trucks listed payload.......how much is left for tongue weight????
And remember until 2013 when SAE J2807 Standards were adopted 'MAX TOW Ratings' were just a magical mfg. marketing tool and had little to do with REAL WORLD towing capabilities.
Based on MAX TOW.....tow vehicles run out of payload, RAWR/REAR Tire Load Ratings and GVWR LONG before ever reaching that magical max tow rating published number
Use REAL numbers........ones that are listed on door jamb stickers and ones from weight scales (something everyone considering towing should do...weigh their vehicle)
SAE J2807 Info