A bookshelf contains \( 6 \) distinct books of Mathematics and \( 5 \) distinct books of Physics. From these \( 11 \) books, \( 6 \) books are chosen at random. Let \( X \) be the absolute value of the difference between the number of Mathematics books chosen and the number of Physics books chosen. If \( \alpha \) is the mean of the random variable \( X \), then the value of \( 77\alpha \) is _________.
