At once, the ratio of male and female members on Brilliant.org was 10:1. \(n\) boys joined to make the ratio 11:1, then \(m\) girls joined to make the ratio 9:1. \( \frac {m}{n}\) could be written as \(\frac {a}{b}\), where a and b are coprime integers. What is \(ab\)?

P.S. I made this question up, and the data in the question may not be correct.

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