$ABCD$ is a convex quadrilateral. Its $AC$ and $BD$ diagonals intersect at point $E$, they are perpendicular to each other. The midpoints of the sides $AD, AB, BC, CD$ are $P, Q, R, S$ respectively. If the diagonals of $MNPQ$ intersect at point $F$ and $AD=5, BC=10, AC=10, BD=11$, then the length of $EF$ can be expressed as $\sqrt {\frac {a}{b}}$, where $a, b$ are coprimes. Find $a+b$.