I never had much luck with that method; the force required to budge the cork is kinda scary.
Someone recently told me a better way: screw the SAK down until it's actually touching the rim of the bottle on both sides, then "rock" the SAK to start the cork, pulling up on one end, then the other. The idea is, the rim acts as a fulcrum, giving you much more leverage. Once the cork starts to move, breaking the seal, it's a lot easier to pull it out as described above by Zwaplat.