Is it a unique triplet?

Algebra Level 5

For some positive integers aa, bb, and cc, we have 2+33=a+b+c2+332+33\large 2+\sqrt[3]{3}=a+\frac{-b+\dfrac{c}{2+\sqrt[3]{3}}}{2+\sqrt[3]{3}} Find a+b+ca+b+c.

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