Nonmanagement rhymes with:
micromanagement, mismanagement, micromanagement, mismanagement, micromanagement, mismanagement, telemanagement, acknowledgement, acknowledgment, discouragement, encouragement, micromanagement, mismanagement, telemanagement
Nonmanagement sounds like:
naismith, nakamoto, nanosecond, nascent, nascimento, negent, neighmond, nesmith, neugent, nicknamed, nishimoto, nugent