For $a \in R$ (the set of all real numbers), $a \neq-1, \lim _{n \rightarrow \infty} \frac{\left(1^a+2^a+\ldots+n^a\right)}{(n+1)^{a-1}[(n a+1)+(n a+2)+\ldots+(n a+n)]}=\frac{1}{60}$. Then $a=$
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