Newton won't help us!

Algebra Level 5

\[\left\{\begin{matrix} 2x+y+4z=5 & & \\ x^2+y^2+z^2+2x+4y+6z=7 & & \\ \left \lfloor (x^{10}+y^{10}+z^{10})(x^{11}+y^{11}+z^{11}) \right \rfloor =? & & \end{matrix}\right.\]

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