What is the average (mean) of all $5$-digit numbers that can be formed by using each of the digits $1$, $3$, $5$, $7$, and $8$ exactly once?The answer is in the form rac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.

Let's think step by step and output the final answer within \boxed{}.
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