Mail failed after name server changed,

Mail failed after name server changed,

Currently MX point to Zoho, but when name server changed (where website is hosted for the domain), Zoho cant identify the MX records. 

My question is, because I am using godaddy, and i can only change the MX record when it is pointed at their own server. So is it not possible to use zoho mail and also have the site hosted elsewhere, say bluehost?