Find the minimum value of the expression: $\displaystyle P=(5a+\frac{2}{b+c})^{3}+(5b+\frac{2}{c+a})^{3}+ (5c+\frac{2}{a+b})^{3}$ where $\displaystyle a,b,c$ are positive real numbers satisfying: $\displaystyle a^{2}+b^{2}+c^{2}=3$
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