I thought at the time it was a good idea to enable brute force sensitivity in WHM on the server. But apparently with the numerous attempts daily, I sometimes find that I am locked out unnecessarily. I had forgotten to whitelist my IPs so that I was inevitably included in the lockout.
Anywho, I learned that I would have to delete the cphulkd tables that contained the offending IPs before I could access my WHM again. Initially I tried disabling cPHulk using the following code, but to no avail:
/usr/local/cpanel/bin/cphulk_pam_ctl --disable
So I used PuTTy to SSH into the server and used MySQL to remove the blocked IP tables.
mysql> use cphulkd;
Expected result: Database changed.
mysql> DELETE FROM `brutes`;
mysql> DELETE FROM `logins
mysql> quit;
Consequently, I was able to get into WHM, enter the Security Center to modify cPHulk Brute Force Protection, and whitelist my IPs.