You could start with a stroke check, like the MOSFUDAT, but since you specifically mentioned "long, difficult cut shots"--and I'm assuming "difficult" mean thin--you need to set the shot up and repeat it. However, focus on hitting it as consistently the same way for several times--even if you miss, you want to miss it similarly each time. You can learn to adjust from that, and decide if it's your aim or mechanics/delivery then, but I would recommend going a step further.
If you also set the "mirror" version of the shot up, you may find that you make the ball more easily, or it's worse. This can point to a vision-center issue, or an alignment issue (could *maybe* call that 'mechanics', but repeating the shot to achieve consistent results is intended to average that out). The idea here is that you may find that you aim/align and/or stroke off-center--even if you don't think you are--and shooting both 'sides' is intended to show if you favor one side. Any 'favoritism' doesn't usually get noticed when playing a game, because it's not usual to compare all of the left cuts vs. right cuts in a game, to compare makes vs. misses.
