I'm wondering how long does it take to cure tmj?

Hard to "cure" Tmj dysfunction can be rather complex. Treatment may be simple or quite involved. Tmj joints, like all other joints, are slower to heal than some other parts of the body. Tmj dysfunction may involve muscle activity levels and their "memory"--habitual pattern of movement, as well as remodeling of the joints. Upon treatment, you may become free from symptoms but TMJ condition will need be monitored.
TMD\TMJ. Tmjoint dysfunction varies widely, may be quite complex ; most dentists have neither the training or experience to treat the more complex cases. 'cure' is the wrong word. Simple, early onset cases are usually easily managed. Chronic, more complex cases are more difficult to 'manage'. Each case is different. Treatment may involve multiple modalities. Find a highly qualified dentist to evaluate u.
Depends. sometimes can be cured in a day. Other times a life long problem which can only be managed.