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