# Mathematical mistakes are interesting

Algebra Level 3

Professor Ávila gave Esmeralda an equation of the form $$ax = b$$, where $$a$$ and $$b$$ are real numbers. Esmeralda, by accident, solved the equation $$bx = a$$ and got a solution that is equal to the correct one minus 60. If the correct solution is of the form $$m + \sqrt{n}$$, where $$m$$ and $$n$$ are integers, what is the value of $$m + n$$?

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