If the non-compete clause is limited to what you have provided here, accepting employment with a competitor is not the same as setting up business as a direct competitor, and is therefore not a breach of the contract/agreement.
If, however, there is more to the non-compete than what you have quote here, you may want to review your circumstances with an attorney in your area. Enforceability if non-compete agreements is specific to the jurisdiction or state in which you are located, and is dictated by statute and by case-law.
I have personally seen non-compete agreements drafted by corporate attorneys in foriegn jurisdictions that can simply be disregarded, as they are wholly unenforceable under current WI case-law -
- the point is, just because there is a non-compete, don't assume that you are stuck with it!