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The natural number $m$, for which the coefficient of $x$ in the binomial expansion of $\left(x^m + \frac{1}{x^2}\right)^{22}$ is 1540, is ____.
${}^{22}C_r = 1540 = {}^{22}C_3$. With $r = 3$: $22m - 3m - 6 = 1$, only $m = 13$ works.
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