Locus is Circle

Level pending

The locus of points which satisfy the system of equations \[\begin{align} x^2+y^2+z^2-2x-4y+2z-19 &= 0, \\ 2x+y+2z &= 11 \end{align}\] is a circle with center \((a, b, c)\). What is \(a+b+c\)?

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