That’s a remarkably good approximation, though it’s missing an extra “ee” at the end (from the i). In particular it is indeed chick not cheek. In both names the l in ly is silent, and the stress is on the first syllable (accent marks don’t denote stress).
EDIT: there is an accent (and a stress!) on the first vowel in Csíkszentmihályi, making it cheek not chick. Oops.
