Let \( \alpha,\beta;\alpha>\beta \) be the roots of the equation \( x^{2}-\sqrt{2}\,x-\sqrt{3}=0 \). Let \( P_{n}=\alpha^{n}-\beta^{n},\, n\in\mathbb{N} \). Then \( \left(11\sqrt{3}-10\sqrt{2}\right)P_{10}+\left(11\sqrt{2}+10\right)P_{11}-11P_{12} \) is equal to
