Let the line $2x+3y-k=0,\ k>0$ intersect the $x$-axis and $y$-axis at points $A$ and $B$, respectively. If the circle having $AB$ as a diameter is $x^{2}+y^{2}-3x-2y=0$ and the length of the latus rectum of the ellipse $x^{2}+9y^{2}=k^{2}$ is $\dfrac{m}{n}$, where $m$ and $n$ are coprime, then $2m+n$ is equal to: