Limit problem

Calculus Level 4

\[ \large \lim_{n\to\infty} \dfrac{1^a + 2^a + 3^a + \cdots + n^a}{(n+1)^{a-1} \left [(na+1) + (na + 2) + \cdots + (na+n) \right ]} \]

Find the sum of all constant values of \(a\) such that the limit above is equal to \( \dfrac1{60} \).

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