$\frac{21^2 + 21 + 1}{21^3-1}= \frac PQ$

The equation above holds true for coprime positive integers $P$ and $Q$ . What is $P+Q$ ?

The answer is 21.

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$\displaystyle \begin{aligned} x^3 - 1 & = \left(x - 1\right)\left(x^2 + x + 1\right) \\ \implies \frac{x^2 + x + 1}{x^3 - 1} & = \frac{1}{x - 1} & \small \color{#3D99F6} \text{Let} \ x = 21 \\ \implies \frac{21^2 + 21 + 1}{21^3 - 1} & = \boxed{\displaystyle \frac{1}{20}} \end{aligned}$