Sum of cube roots of a cubic’s roots

This is a standard question to prepare for India’s famously challenging JEE Advanced exam. Here is one way to solve the question quickly. Thanks to Avinash for the suggestion! Special thanks this month to: Daniel Lewis, Robert Zarnke, Kyle, Mike Robertson. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions

Problem credit to David Altizio (section 3 Geometry, problem 66):
https://davidaltizio.web.illinois.edu/HomemadeProblems.pdf

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