Strictly speaking, most of SDN literature does not address the "management plane" as you have mentioned in the question. Control plane and its separation from data plane gets the bulk of the focus.
As rightly mentioned by CaptainCap above, the management plane is the interface between User (Network admin/ops to be precise) and devices. Also, it's not just limited to configuring of devices, but also monitoring the devices by gathering information from them from time to time (classic NMS function) and generating reports based on the data collected. This in turn can help network administrators identify potential problems / trends and take corrective action - in the form of short term fixes / long term solutions. This kind of monitoring / data collection is not part of control plane, and I am not sure how/if it can fit the "north bound / south bound" API model within the SDN architecture.
Check out this article, though old, does point to the same thing - https://www.sdxcentral.com/articles/contributed/does-sdn-make-my-network-management-look-fat/2012/09/