A Pre-RMO question! -27

Geometry Level 2

Let $\overline{AH},\overline{AD}$ and $\overline{AM}$ be an altitude, an angle bisector, and a median of $\triangle ABC$ . If $\overline{AB}=14$ , $\overline{AC}=10$ , $\overline{BC}=18$ , and the area of $\triangle ADM$ is $\dfrac{7\sqrt{k}}{4}$ , find value of $k$ .