We investigate theoretically shot noise in an artificial Single Molecule Magnet based upon a CdTe quantum dot doped with a single S=5/2 Mn spin and gated in the hole sector. Mn-hole exchange anisotropy is shown to lead to profound consequences on noise, like super-Poissonian behaviour. We report on a novel effect, similar to the Dicke effect in Quantum Optics, that allows to separately extract the hole and Mn spin relaxation times using frequency-resolved shot noise measurements. We expect that

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... our findings may have further relevance to experiments in other S>1/2 systems including transport through Mn(12) molecules and STM spectroscopy of magnetic atoms.