Olympiad Geometry · Challenge problem

Cube $ABCDEFGH$ has edge $6$, with square $ABCD$ on the bottom and $E$, $F$, $G$, $H$ directly above $A$, $B$, $C$, $D$. Let $M$ be the midpoint of edge $\overline{AE}$. The plane through $B$, $D$ and $M$ slices the cube. Find the area of the cross-section, in simplest radical form.