Reciprocals of the Roots

Determine the value of $\frac{1}{m}+\frac{1}{n}$ if $m$ and $n$ satisfy the equation $x^2 - 3x + 1 = 0$. The answer is in the form $\frac{\alpha}{\beta}$ for coprime integers $\alpha$ and $\beta$. Input the answer as the sum $\alpha +\beta$.