\[\large f\left( x \right) =\sqrt { 21+4x-{ x }^{ 2 } } -\sqrt { 10+3x-{ x }^{ 2 } } \]

If the maximum value of the function given above occurs at \(x={ x }_{ 0 }\) and the maximum value is \({y }_{ 0 }\), find \({ x }_{ 0 }+{ y }_{ 0 }\).

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