Each of two boxes contains both black and white marbles, and the total number of marbles in the two boxes is \(25.\) One marble is taken out of each box randomly. The probability that both marbles are black is \(\frac{27}{50},\) and the probability that both marbles are white is \(\frac{m}{n},\) where \(m\) and \(n\) are relatively prime positive integers. What is \(m + n\)?

(第十八届AIME1 2000 第5题)