For many years, students were taught to never split infinitives, as I have just done, despite the split infinitive breaking no grammatical rule. Some now deride the rule as an example of how English teachers liked to torture us for no good reason, but few pity the poor teacher who used this rule and others to encourage students to study their own writing with a critical eye rather than to rely on easy, lazy, and poor habits. Yes, splitting an infinitive is grammatically all right, but that does not mean you always want to split your infinitives.
To split an infinitive is to remove emphasis from the verb and place it on the adverb—often a weak, unemphatic, and unnecessary crutch of insecure writers; many adverb-verb combinations can be replaced with a more specific and succinct verb. Splitting an infinitive can, however, be useful to form a more approachable voice. An example from The Elements of Style captures this well: “I cannot bring myself to really like the fellow” would sound unnecessarily formal, given the tone of the sentence, if the infinitive were not split.
I suggest keeping your infinitives together unless rhythm, sound, or emphasis convinces you otherwise; it requires a practiced ear to recognize when to split and not to split an infinitive.