I'm not sure what you calling a "Brinly Hitch". The Cub Cadet needs to have what IH called a 3 point hitch on it. That consist of upper casting that has a 1" diameter hole for a "pin" about 8" long in it, and is connected to the deck/implement lift arm of the tractor by a flat bar that runs inside the right frame rail. That 1" pin is 1 point of the IH 3 point hitch. There is also a "C" shaped bracket about 10"-11" long with 90 degree bends in each end (that make the C shape) bolted to the bottom of the of the transmission using the bottom 3 bolts of the rear cover. There are 3 vertical bolt holes in the 90 degree bends.
This bottom bracket with the holes in the bends make the othet 2 points of the 3 point IH hitch. You still with me?
To connect a plow or other sleeve hitch implement, you also need a Brinly-Hardy Sleeve Hitch adaptor (no longer made, but was model HH-150 Implement Hitch). This is "U" shapped, about 12" long and wide enough to fit on the outside of the "bends" of the bottom 3 point bracket. In the rear center of this "U" is a vertical "pipe" and flat stock bracket. This U adaptor bolts or pins to the bottom 3 point bracket. There are 2 flat stock (about 1-1/4" W x 12" or so long) bars/straps with several holes and or a slot that are used for adjustment, that pin to the flat stock bracket at the rear of the U, and the other end is connected or pinned to the 1" diameter pin that goes in the hole in the upper casting. With that all connected, moving the tractor lift arm will inturn raise or lower the U shapped Brinly adaptor.
The plow or implement then connects to the adaptor by sliding the sleeve hitch (the "C" shapped part on the front of your plow that needs to be cut off, turned 90 dedrees and rewelded) over the verticle pipe in the rear center of the U, and connected together with a hitch pin. There are two bolts on either side of the pipe that will tighten against the sleeve hitch to limit/prevent the implement was swinging side to side. The piece that is on the front of your plow that has 2 or 3 bolts in it and pivots in the rotated sleeve hitch is not part of the assembly and would not be used. The plow as it is shown does not have a Brinly model number as far as I can find. The basic sleeve hitch plow with coulter is model number PP-508, PP-510, or PP-512, depend on if it is an 8", 10", or 12" plow. Here are some pictures that may help, or you can go here; http://www.cubcadetcollectors.com/forum ... php?cat=18
,scroll down to and click on the Brinly Plow or Sleeve hitch, when the page opens typr the word yellow in the box in the lower right, click the picture and it will open the manual in a PDF format .