Unless your basic truck weight is high, as in having a service body mounted, running high pressure in your unloaded truck has no advantage. The higher pressures only make the tire less able to absorb regular bumps, and irregularities in your everyday driving, resulting in a harsher ride. Even more so in LT rated tire with it's stronger stiffer construction.
The purpose of max inflation rating is when the tire is carrying it's maximum load, to keep the proper tire profile.
There's a little item for the guys that always tow way over truck capacity, your not just over what the trucks designed for, your probly exceeding the capability of your tires.
And their is, unless it's been scraped off, a tag in driver's door jam that has tire size it left the factory with and tire inflation. Good luck.