This is a wild guess, but I've seen it on 2 other F series trucks. But check the torque converter bolts. Make sure they are all there and tight.
It sounds like they may have come loose.
The only other thing I can recommend is to pull the belt and visually inspect each pulley, including the balancer/dampner itself.
Then start the engine (don't run very long, only long enough to see if the noise goes away) and see if the noise is still there. If it is, then you have confirmed that it isn't accessory drive pulley that ins't making the noise.
If it is still there and you have inspected the torque converter bolts, my next place to be considering checking would be a timing chain problem.
You have to do the process of elimination, unless you can pinpoint the actual location of the noise.