Let $n$ be the smallest positive integer such that $mn$ is a perfect $k$th power of an integer for some $k \ge 2$, where $m=2^{1980} \cdot 3^{384} \cdot 5^{1694} \cdot 7^{343}$. What is $n+k$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $n$ be the smallest positive integer such that $mn$ is a perfect $k$th power of an integer for some $k \ge 2$, where $m=2^{1980} \cdot 3^{384} \cdot 5^{1694} \cdot 7^{343}$. What is $n+k$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
13
Let $n$ be the smallest positive integer such that $mn$ is a perfect $k$th power of an integer for some $k \ge 2$, where $m=2^{1980} \cdot 3^{384} \cdot 5^{1694} \cdot 7^{343}$. What is $n+k$?
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