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Given that the zeroes of the cubic polynomial \(x^3 - 6x^2 + 3x + 10\) are of the form \(a\), \(a + b\), \(a + 2b\) for some real numbers \(a\) and \(b\), find the values of \(a\) and \(b\) as well as the zeroes of the given polynomial.
 
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This is a self-assessment task. Solve this question and assess the solution steps after completing the test on your own.