Bag A contains \( 2 \) white, \( 1 \) black and \( 3 \) red balls and bag B contains \( 3 \) black, \( 2 \) red and \( n \) white balls. One bag is chosen at random and \( 2 \) balls drawn from it at random, are found to be \( 1 \) red and \( 1 \) black. If the probability that both balls come from Bag A is \( \frac{6}{11} \), then \( n \) is equal to ________.
