$$6 \cdot \frac{x-11}{5} = 5 \cdot \frac{x+11}{6}$$

$$ \begin{aligned} 6 \cdot \frac{x-11}{5} &= 5 \cdot \frac{x+11}{6}&& \text{multiply ALL terms by } \color{blue}{ 30 }. \\[1 em]30\cdot6 \cdot \frac{x-11}{5} &= 30\cdot5 \cdot \frac{x+11}{6}&& \text{cancel out the denominators} \\[1 em]36x-396 &= 25x+275&& \text{move the $ \color{blue}{ 25x } $ to the left side and $ \color{blue}{ -396 }$ to the right} \\[1 em]36x-25x &= 275+396&& \text{simplify left and right hand side} \\[1 em]11x &= 671&& \text{ divide both sides by $ 11 $ } \\[1 em]x &= \frac{671}{11}&& \\[1 em]x &= 61&& \\[1 em] \end{aligned} $$

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