In the compound \( \text{MnO}_4^- \), the oxidation state of manganese (Mn) is +7. When \( \text{MnO}_4^- \) is reduced to \( \text{Mn}^{2+} \), the oxidation state of manganese decreases to +2.
This is a reduction process, as the manganese atom gains electrons, reducing its oxidation state.
Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.