I have a kitchen cabinet with 18" drawers, with slides on the side. The internal depth of them is 23" as is the length of the part of the slide mounted to cabinet.
The inside of my cabinet looks like this:

My drawer looks like this:

I wish to replace the slides because the rear mount is cracked like so:

So my question is will this 22" slide, this rear bracket and this frame mounting bracket work? There only seems to be 22" and 24" brackets and I assume I am somehow measuring wrong.
Replacing just the bracket is an option, but quite frankly none of my drawers in my kitchen slide very smoothly so I'm looking to replace all of them.