An acoustic metamaterial (AMM) consisting of a porous material (melamine foam) layer above a symmetrical labyrinthine metamaterial, incorporating a micro-hole and micro-slit cover plate, is proposed to simultaneously mitigate low and high frequency noise from industrial machineries. Theoretical model of sound absorption by this AMM is developed and validated numerically and experimentally. Sensitivity analysis indicates that increasing the length of the labyrinthine pathway and cover plate thickness and decreasing the slit width, slit length, and hole diameter shifts the peak sound absorption to lower frequencies. This material is successfully applied as a sound absorptive enclosure of a 0.5 hp water pump to reduce its sound pressure levels across widely separated frequencies of 1414-2245 Hz (high frequency) and 176-222 Hz (low frequency). This study offers guidelines to noise control engineers for controlling low and high frequency noise in industrial machineries.