"effectively manage" is a correct and usable phrase in written English.
You could use it to describe how to do something, such as: "We must effectively manage our resources in order to ensure success."
Trained EM physicians can safely and effectively manage trauma patients and perform advanced airway management.
YSCP strives to more effectively manage energy use and mitigate climate change through energy management systems.
Can you suggest methods to more effectively manage this?
Contingent workers effectively manage their time and meet deadlines.
"There's no way for me to effectively manage that risk".
There are ways to reduce, or at least more effectively manage, medical debt.
Unless we effectively manage drug use in this country, everything else is fire-fighting".
That makes a big difference in our ability to effectively manage the building".
Women should ideally be given the minimal amount of therapy necessary to effectively manage symptoms.
This is an aggressive response, but it shows that boards can effectively manage the sale process.
Yet once they put this in place, they failed to properly control it and effectively manage it.
