Minimize $x+y$ given $(C - 1)xy + x=D$

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Minimize $x+y$ given $(C - 1)xy + x=D$ where $x$ and $y$ are positive reals

I am looking to derive an equation such that given a constant $C$ and an objective value $D$, I am able to determine the minimum needed combined $x$ and $y$ to reach it.

objective function with a horizontal plane at D