What number should be added to $\dfrac{-2}{3}$ to get $\dfrac{-1}{7}$?

Let the required number be $x$.

According to the given condition,

$\Rightarrow \dfrac{-2}{3} + x = \dfrac{-1}{7} \\[1em] \Rightarrow x = \dfrac{-1}{7} - \left(\dfrac{-2}{3}\right) \\[1em] \Rightarrow x = \dfrac{-1}{7} + \dfrac{2}{3} \\[1em] [\text{ LCM of } 7 \text{ and } 3 = 21] \\[1em] \Rightarrow x = \dfrac{(-1) \times 3 + 2 \times 7}{21} \\[1em] \Rightarrow x = \dfrac{-3 + 14}{21} \\[1em] \Rightarrow x = \dfrac{11}{21}$

Hence, the required number is $\mathbf{\dfrac{11}{21}}$.