In the figure given below, $P$ is a point on $AB$ such that $AP:PB=5:4$. $PQ$ is parallel to $AC$ and $QD$ is parallel to $CP$. $AR$ and $QS$ are perpendicular to $CP$. Length of $QS=6$ then ratio of $AP:PD=a:b$ where $a,b$ are relatively co-prime and positive number. Then $a+b=?$