An Overlap of Congruent Triangles

Points $C$ and $D$ lie on the same side of the line $AB$, with $\triangle ABC\cong\triangle BAD$, $AB=9$, $BC=AD=10$, and $CA=DB=17$. The area of the intersection of the two triangles, written as a fraction in lowest terms, is $\dfrac mn$. Find $m+n$.