$$ \begin{aligned} n-\frac{5}{6}+n+\frac{3}{7} &= \frac{11}{21}&& \text{multiply ALL terms by } \color{blue}{ 42 }. \\[1 em]42n-42\cdot\frac{5}{6}+42n+42\cdot\frac{3}{7} &= 42\cdot\frac{11}{21}&& \text{cancel out the denominators} \\[1 em]42n-35+42n+18 &= 22&& \text{simplify left side} \\[1 em]84n-17 &= 22&& \text{ move -17 to the right } \\[1 em]84n &= 22+17&& \\[1 em]84n &= 39&& \text{ divide both sides by $ 84 $ } \\[1 em]n &= \frac{39}{84}&& \\[1 em]n &= \frac{13}{28}&& \\[1 em] \end{aligned} $$

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