Let points $A=(0,0)$, $B=(1,3)$, $C=(3,4)$, and $D=(4,0)$. Quadrilateral $ABCD$ is cut into equal area pieces by a line passing through $A$. This line intersects $\overline{CD}$ at point $\left(\frac{p}{q},\frac{r}{s}\right)$, where these fractions are in lowest terms. What is $p+q+r+s$?