When a certain biased die is rolled, a particular face occurs with probability \(\frac{1}{6}-x\) and its opposite face o…

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 \(\operatorname{sum}=7\), when such a die is rolled twice, is \(\frac{13}{96}\), then the value of \(x\) is:

[JEE Main 2021, 27 Aug (Shift 1)]