\[x - \frac{10x + 1}{6} = \frac{4x + 1}{6}\ \ \ | \cdot 6\]
\[6x - 10x - 1 = 4x + 1\]
\[- 4x - 4x = 1 + 1\]
\[- 8x = 2\]
\[x = - \frac{1}{4}.\]