# Plastic!

Algebra Level 5

Let $$\Lambda$$ be a real number that can be represented in the nested radical form as

$\Lambda = \sqrt[3]{1 + \sqrt[3]{1 + \sqrt[3]{1 + \cdots}}}$

If the closed form of $$\Lambda$$ is

$\Lambda = \displaystyle {\frac {{\sqrt[{3}]{a+b{\sqrt {c}}}}+{\sqrt[{3}]{a-b{\sqrt {c}}}}}{d}}$

where $$a, b, c$$ and $$d$$ are positive integers with $$c$$ square-free. Find the smallest possible value of $$a+b+c+d$$.

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