Is it legal to install a personal copy of Final Cut Pro X on my work computer?
You need a lawyer to decode the legality of a license coupled with the local and state and national laws where you live.

As far as decoding the licensing terms - focus on who purchased the app in Apple's eyes. If you as a consumer (non-commercial use) bought the app, then I would say you are totally in the clear installing it on computers you control especially if others are not using the computers you control and that software at the same moment as you are and if you don't lease out that app or sell/rent it. If you have 15 macs at home and one at work, there is nothing I see in the EULA that says you can't install Final Cut Pro on all of them for your sole use.