Ahaan's polynomial roots

Algebra Level 4

Suppose \( u \), \( v \), and \( w \) are the roots of polynomial \[ f(x) = x^3 + 20x^2 + 13x + 42, \] and \( \frac {1}{u} \), \( \frac {1}{v} \), and \( \frac {1}{w} \) are the roots of polynomial \[ g(x) = x^3 + rx^2 + sx + t. \] If \( g(1) = \frac {a}{b} \), where \( a \) and \( b \) are coprime positive integers, what is the value of \( a + b\)?

This problem is posed by Ahaan Rungta.

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