Let \( C_{1} \) be the circle in the third quadrant of radius \( 3 \), that touches both coordinate axes. Let \( C_{2} \) be the circle with centre \( (1,3) \) that touches \( C_{1} \) externally at the point \( (\alpha,\beta) \). If \( (\beta - \alpha)^{2} = \frac{m}{n} \), \( \gcd(m,n)=1 \), then \( m+n \) is equal to:
