If $A$ is a $2 \times 2$ matrix such that $\det(A) = 3$ and $A^{-1} = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$, what is $a+d$ (the trace of $A^{-1}$) if $A = \begin{pmatrix} 1 & 2 \\ 1 & 5 \end{pmatrix}$?