[verb ます-stem] + 切れない [verb ます-stem] + 切れる
切れない goes on a verb's ます-stem and means you can't do all of something: more food than you can finish, more stars than you can count. It is the negative of きれる切れる, "can do completely", which is the potential of きる切る.
The verb is in the ます-stem, not the dictionary form: ×食べる切れない. 切れない conjugates like any ない-form: きれなかった切れなかった, きれません切れません, きれませんでした切れませんでした. It is often written in kana, たべ食べきれない.
切れない says the action is possible but there is too much of it to get to the end. The plain potential, たべられない食べられない, says you can't do it at all – because of an allergy, a dislike, or the food being inedible.
These go beyond too much to finish.
Without the negative, the pattern says you can get through all of it.
With verbs of saying and expressing, the meaning is "can't put all of it into words": あらわし表しきれない切れない, かたり語りきれない切れない. いいきれない言い切れない is different: いいきる言い切る means "state flatly", so 言い切れない is "can't say for certain".