If you managed a perfect inverse of the wave, the two waves will cancel enough other out and there will be no sound at all. This means that, with perfect noise cancelation, you could be sitting right on top of a jet engine and would hear nothing and have no damage occur.

Practically, getting a perfect inverse is impossible. You'd need a speaker perfectly aligned between the source of the sound and your ears, and the source will actually be a bunch of different points inside the engine, meaning you need roughly an infinite number of infinitely small speakers and microphones.

I did find a video that shows how the phasing works. Its worth noting that the antiphase (opposite) sound will sound the same as the original if heard on its own.