\[x_{1}\ и\ \ x_{2} - корни\ уравнения.\]
\[x_{1} + x_{2} = - 7;\ \ \ \ x_{1} \cdot x_{2} = - 11.\]
\[x_{1}^{3} + x_{2}^{3} =\]
\[= \left( x_{1} + x_{2} \right)\left( x_{1}^{2} - x_{1}x_{2} + x_{2}^{2} \right) =\]
\[= \left( x_{1} + x_{2} \right)\left( x_{1}^{2} + x_{2}^{2} - x_{1} \cdot x_{2} \right) =\]
\[= - 7 \cdot \left( 71 - ( - 11) \right) =\]
\[= - 7 \cdot 82 = - 574\]