It really depends on the type nut that is in there. If it is a long nut that has the inside hex where allen wrench fits then you can back it out with the wrench. If the wrench keeps turning the nut but it still will not back out but only turns, then an easy out will grab the inner hollow of the nut which will give you some hope of pull while you turn it counter clockwise.

Needle nose pliers, or anything that will grip the nut and pull it outward while it turns. But remember, even after the nut is removed we still have the strip threads on the end of the rod. Sometimes you might be able to find a nut that is undersized a little and maybe be able to get it to rethread itself onto the rod threads. A stainless nut is much harder than the mild stell on the rod so it should recut the threads to match the nut but you must only turn it clockwise a small amount allowing it to cut into the mild steel rod end and then reverse it and then do this back and forth going a little tighter each time as you are carving new threrads on the end of the rod.

Again this all depends on what type nut is there. In some cases it is worth trying bexause otherwise you have to replace the neck or take the fretboard off the neck, re-insert a new rod, then put the fretboard back on the neck. It also depends on how much damage was done to the threads on the rod. Always when tightening a truss rod be sure the string tension is very loose. If the string are still tight and tuned then you have a lot of pressure working against the tightening and you have to over force and that's what strips threads and breaks rods.

The easy out is only a suggestion of a way to remove the stripped nut. I would not use a drill as this would turn the nut too fast. In some cases the rod can be pulled out of the neck but only if the neck wwas built in such a way as the rod can slide out. Most of the time it's best to just take the fretboard off and replace the entore rod but often times the guitar may to low end value to do such repairs. It is a real challenge no doubt.