# Random reals.

Algebra Level 4

$$a,b,c$$ are positive real numbers such that $$\dfrac{1}{b+c} + \dfrac{1}{c+a} + \dfrac{1}{a+b} = 1$$. If the minimum value of $$\dfrac{1}{a^5} + \dfrac{1}{b^5} + \dfrac{1}{c^5}$$ can be written as $$\dfrac{p}{q}$$ where $$p$$ and $$q$$ are positive integers with $$\text{gcd(p,q)}=1$$, find $$(p+q)$$

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