Absolutely yes, you need to tell the company. And expect them to forbid this.
OK, let me walk that back a bit. You should probably talk to a lawyer, but I'm fairly sure the answer will be a) yes you need to tell them b) they are going to own everything you do in this area c) they won't want you working on this on your own.
Put simply, this is a conflict of interest. If you have a bright idea in the shower one day about how to solve problem X, is that idea your property or theirs? The company definitely want it to be theirs. You would have to make a decision whether to act in the company's interests or your own, and you never want to be in that kind of position. If they are hiring you to work on problem X they also want everything you currently know about it to be available to them. Are you going to be telling them everything you know?
You might get away with this if your area of work unquestionably never overlaps with Problem X, and that you never talk to anybody at the company who might have knowledge of their problem X solutions, and you can prove that in court under questioning from the company's highly paid lawyers.
Even if you do everything absolutely legitimately the company may well try to shut down your startup if it competes with them. And unless you are an exceptionally rich startup they may succeed for long enough to cripple your startup, even if the law is not actually on their side.