JEE Main 2021 — Probability Question with Solution

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