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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