When a certain biased die is rolled, a particular face occurs with probability 1/6-x and its opposite face occurs with probability 1/6+x. All other…

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