Find the integer closest in value to
\[\frac{1}{\sqrt[4]{5^4+1}-\sqrt[4]{5^4-1}}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the integer closest in value to
\[\frac{1}{\sqrt[4]{5^4+1}-\sqrt[4]{5^4-1}}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
250
Find the integer closest in value to
\[\frac{1}{\sqrt[4]{5^4+1}-\sqrt[4]{5^4-1}}.\]
train