Rewrite a problem for the third time.

$a$ , $b$ and $c$ are three positives such that $9 < (a + b + c)\left(\dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c}\right) = n$ is constant and the following inequality is correct for $\forall a, b, c \in \mathbb Z_+$ .

$\large m \le (a^2 + b^2 + c^2)\left(\dfrac{1}{a^2} + \dfrac{1}{b^2} + \dfrac{1}{c^2}\right) \le (n - 10)^2$

Calculate the value of $m$ .