Average Value Over All Permutations

Let $ S(M, T, A, P, L) = 2M - 3T + AP + L $. For each permutation of the values $ (1, 2, 3, 4, 5) $ into the ordered 5-tuple $ (M, T, A, P, L) $, the value of $ S(M, T, A, P, L) $ is obtained. There will be $ 5! = 120 $ values obtained this way. What is the average of all those values? The answer is in the form $\frac{\alpha}{\beta}$ where $\alpha$ and $\beta$ are coprime positive integers. Input the value of $\alpha + \beta$.