Six random variables

Six variables \( x_i \) are chosen uniformly at random in the interval \([0,1]\).

Find the probability that \[ x_1 + x_2 + x_3 + x_4 + x_5 + x_6 < 1. \] If the answer is of the form \(\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, what is \(a+b?\)


Inspired by Brian Charlesworth
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