A superconducting-to-magnetic transition is reported for LaFe$_{1-x}$Mn$_x$AsO$_{0.89}$F$_{0.11}$ where a per thousand amount of Mn impurities is dispersed. By employing local spectroscopic techniques like muon spin rotation (muSR) and nuclear quadrupole resonance (NQR) on compounds with Mn contents ranging from x=0.025% to x=0.75%, we find that the electronic properties are extremely sensitive to the Mn impurities. In fact, a small amount of Mn as low as 0.2% suppresses superconductivity completely. Static magnetism, involving the FeAs planes, is observed to arise for x > 0.1% and becomes further enhanced upon increasing Mn substitution. Also a progressive increase of low energy spin fluctuations, leading to an enhancement of the NQR spin-lattice relaxation rate 1/T1, is observed upon Mn substitution. The analysis of 1/T1 for the sample closest to the the crossover between superconductivity and magnetism (x = 0.2%) points towards the presence of an antiferromagnetic quantum critical point around that doping level.