Integer Equations

x,\color{#3D99F6}{x}, y,\color{#D61F06}{y}, and z\color{#20A900}{z} are integers, and xyz=10.\color{#3D99F6}{x}\color{#D61F06}{y}\color{#20A900}{z}=10. What is the maximum possible value of x+y+z?\color{#3D99F6}{x}+\color{#D61F06}{y}+\color{#20A900}{z}?

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