Probability

When a certain biased die is rolled, a particular face occurs with probability ${1 \over 6} - x$ and its opposite face occurs with probability ${1 \over 6} + x$. All other faces occur with probability ${1 \over 6}$. Note that opposite faces sum to 7 in any die. If 0 < x < ${1 \over 6}$, and the probability of obtaining total sum = 7, when such a die is rolled twice, is ${13 \over 96}$, then the value of x is :