# Sum and Square Sum

Algebra Level 5

$$(x, y, z) \in \mathbb{R}^3$$ are points that lie on the plane $$x + 2y + 3z = 78$$, and lie on the sphere $$x^2 + y^2 + z^2 = 468$$. The maximum value of $$x$$ has the form $$\frac {a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers. What is the value of $$a+b$$?

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