We introduce a new concept of split-ball resonator as a nontrivial generalization of more familiar split-ring resonator composing electromagnetic metamaterials. We realize this novel concept experimentally by employing the laser-induced transfer method to product near-perfect spheres and helium ion beam milling to make cuts with the nanometer resolution. Due to high quality of the spherical particle shape, governed by strong surface tension forces during the laser transfer process, and the clean, straight side walls of the cut made by helium ion milling, magnetic resonance is observed at 600nm in gold and 565nm in silver nanoparticles. We demostrate a strong omnidirectional magnetic dipole response, for both gold and silver spherical plasmonic nanoparticles with nanometer-scale cuts, and also realize tunability of the magnetic dipole resonance throughout the visible spectral range by a change of the depth and width of the nanoscale cut. Structuring arbitrary features on the surface of ideal spherical resonators with nanoscale dimensions provides new ways of engineering hybrid resonant modes and ultra-high near-field enhancement.