$$ \begin{aligned} 6x+\frac{6}{5} &= 5x+1&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5\cdot6x+5\cdot\frac{6}{5} &= 5\cdot5x+5\cdot1&& \text{cancel out the denominators} \\[1 em]30x+6 &= 25x+5&& \text{move the $ \color{blue}{ 25x } $ to the left side and $ \color{blue}{ 6 }$ to the right} \\[1 em]30x-25x &= 5-6&& \text{simplify left and right hand side} \\[1 em]5x &= -1&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= -\frac{1}{5}&& \\[1 em] \end{aligned} $$

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