Let $A$ be a $2 \times 2$ symmetric matrix such that $A \left[ \begin{array} { l } 1 \\ 1 \end{array} \right] = \left[ \begin{array} { l } 3 \\ 7 \end{array} \right]$ and the determinant of $A$ be 1 . If $A ^ { - 1 } = \alpha A + \beta I$, where $I$ is an identity matrix of order $2 \times 2$, then $\alpha + \beta$ equals $\_\_\_\_$