Roots got mad!

Algebra Level 5

Let \(x\) be a real positive number in the interval \( \dfrac{153}{6} \leq x \leq \dfrac{398}{6} \). The maximum value of \( \sqrt{x-1} + \sqrt{2x - 51} + \sqrt{199 - 3x} \) is \(s\) and obtained when \(x = t\). Find \(s + t \).

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