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.

Apple Legal Issue: Should be OK

As noted from the original posters Apple's Terms and Conditions quote it looks like installing Final Cut Pro X on your work computer that you control is allowed by Apple.

The Final Cut Pro X license agreement states that you are granted a limited non-exclusive license to install and use the Apple Software only on Apple-branded computers that you own or control in accordance with the Mac App Store Product Usage Rules located at http://www.apple.com/legal/itunes/ww/ ("Mac Usage Rules"). Except as permitted under the Mac Usage Rules, you may not distribute or make the Apple Software available over a network where it could be used by multiple devices at the same time.

So you will probably not have anyone contacting you from Apple Legal, however I am no lawyer so thats the best that I can say on it.

Employer Legal Issue: ??? (Depends on your employers policies, most employers would not want their employees using their hardware for other work.)

Now, the other gray area to consider is how your employer intends for you to use their hardware. They may not allow or want you to install software or use their computer for side work that's not contributing to their bottom line. So I would check with your employer and ask them if you can use their computer for side work. They may not want you mixing a personal business with their educational business, especially doing so on their hardware dime. Consequences of missing this point could be sever like being fired, so do make sure that you are not violating your user agreement and terms of use for an employer owned computer.

So after legally verifying that you are ok on those two fronts you should be ok to install Final Cut Pro in a completely legitimate fashon.