I'll probably have to go to the dentist tomorrow.

Literal

Tomorrow [topic-は] dentist [to-へ] go-must [probably-でしょう].

いかねばならない is a slightly literary variant of いかなければならない — using the classical negative ~ね (= ない) + ば. Combined with ~でしょう for probability. 歯医者 ('dentist') uses the kanji for tooth + doctor.