The following four points lie on a sphere in the \(xyz\) coordinate system. Coordinates are approximated to three decimal places.

\((x_1,y_1,z_1)\) | \((5.000,8.732,15.000)\) |

\((x_2,y_2,z_2)\) | \((2.000,7.000,17.000)\) |

\((x_3,y_3,z_3)\) | \((3.732,4.000,15.000)\) |

\((x_4,y_4,z_4)\) | \((0.653,10.702,13.695)\) |

If the center of the sphere has coordinates \((h,k,m)\), determine \(h+k+m\).

**Details and Assumptions:**

Round \(h\), \(k\), and \(m\) individually to the nearest integer before adding them.

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