Quadrilateral inside Triangle

Geometry Level 4

In $\triangle ABC$ , $\angle A = 90^\circ$ , $AC = 3$ and $AB=4$ . $CD$ is the angle bisector of $\angle ACB$ . Point $E$ on $AC$ is such that $CE=AE$ . $CD$ and $BE$ intersect at $M$ . If the area of quadrilateral $ADME= \dfrac ab$ , where $a$ and $b$ are positive coprime integers, find $a+b$ .