The function $f(x)$ is defined on the reals such that \( f\left(\frac{1-4x}{4-x}\right) = 4-xf(x) \) for all \( x \neq 4 \). There exist two distinct real numbers \( a, b \neq 4 \) such that \( f(a) = f(b) = \frac{5}{2} \). The sum \( a+b \) can be represented as \( \frac{p}{q} \) where \( p, q \) are relatively prime positive integers. Find \( 10p + q \).

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