Do I need to leave China if I switch from a teaching visa to a student X type?

Mikee, you can try to convert your current work Z type to a student X type at the exit and entry administration of the local PSB within China. If it can be done, you don't need to leave China.
You should prepare the relevant documents including your passport and its copy, the application form, a passport-style photo, valid registration form of temporary residence, admission letter and JW form from the school as well as the physical examination record.