"Happy the man who has never been told that it is wrong to split an infinitive: the ban is pointless. Unfortunately, to see [the rule] broken is so annoying to so many people that you should observe it."
— The Economist Style Guide
The verb you look up in a dictionary is the infinitive form of the verb. It is the present tense form, such as teach, sing, or play.When an infinitive appears with the preposition "to," it forms something called a periphrastic phrase. Many people have been taught to accept this phrase and not separate it with any other words, such as an adverb. In reality, people do this all the time, and it isn't grammatically incorrect. However, to make most readers happy, you may want to keep the phrase together.
"Correct" form: The turtle does not want to eat the fish.
"Incorrect" form: The turtle does not want to quickly eat the fish.
"Best" form: The turtle does not want to eat the fish quickly.