Let the line \( 2x+3y-k=0,\,k>0 \), intersect the \( x \)-axis and \( y \)-axis at the points \( A \) and \( B \), respectively. If the equation of the circle having the line segment \( AB \) 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 \( \frac{m}{n} \), where \( m \) and \( n \) are coprime, then \( 2m+n \) is equal to:
