For real numbers $x$, let 
$$f(x) = \frac{4^x}{25^{x+1}} + \frac{5^x}{2^{x+1}}.$$ 
Then, 
$$f\left(\frac{1}{1 - \log_{10} 4}\right) = \frac{m}{n},$$ 
where $m$ and $n$ are relatively prime positive integers. Find $m + n$.

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