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
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