Solution

When we add two like fractions, the numerators of the fractions gets added and the denominator remains the same. $$~~~\frac{1}{6}+\frac{x}{6}=\frac{5}{6}$$ $$\Rightarrow \frac{1+x}{6}=\frac56$$ From this expression, it is clear that \((1+x)\) must be equal to \(5\).
 $$\displaylines{\therefore 1+x = 5 \\ ~~~~~~\Rightarrow ~~~~~x=5-1\\ \Rightarrow ~~~~~x = 4}$$