Cube roots escape

Algebra Level 5

5343×3=a3+b3c3, \sqrt{\sqrt[3]{5}-\sqrt[3]{4}} \times 3 = \sqrt[3]{a} + \sqrt[3]{b} - \sqrt[3]{c},

where a,ba, b and cc are positive integers. What is the value of a+b+ca+b+c ?

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