$\large \sqrt[3]{2-x}=1-\sqrt{x-1}$ Let $$\alpha,\beta,\gamma$$ be the real roots of the equation above that satisfy the inequality $$\alpha<\beta<\gamma$$. If $$\dfrac{\alpha^2+\beta^2+\gamma^2}{\gamma^2-\beta^2-\alpha^2}=\dfrac{m}{n}$$, where $$m$$ and $$n$$ are coprime positive integers such that $$m>n$$, find $\bigg\lfloor\frac{(m.n)^{m-n}}{m+n}\bigg\rfloor.$