Holiday Contest 2025 - Guts Round - Set 3 Problem 2

Let x and y be real numbers such that

\log_{25} x = \log_{20} y = \log_{16} (24x-20y).

Given that the value of \sqrt{6-\frac{5y}{x}} can be written as \sqrt{a}-b for positive integers a and b where a is not divisible by the square of any prime, find a+b.