Unless that's a shadow, am I seeing 3 wires? I see one red and 2 black? 
Naw, it looks like a shadow. 
Anyhow my guess is the RED is positive which is the TIP of your patch cable or the none braided wire when you open a patch cables jack to take it apart. 
 
So an option is to sacrifice a patch cable, wack the end off or just un soldier it from the jack and soldier that to the wires inside the speaker after you cut them free from the broken jack. 
 

Cactus Music
Unless that's a shadow, am I seeing 3 wires? I see one red and 2 black? 
Naw, it looks like a shadow. 
Anyhow my guess is the RED is positive which is the TIP of your patch cable or the none braided wire when you open a patch cables jack to take it apart. 
 
So an option is to sacrifice a patch cable, wack the end off or just un soldier it from the jack and soldier that to the wires inside the speaker after you cut them free from the broken jack. 
 

Nope - used flash so it may give the appearance of a third wire. But thanks, Cactus! This is the exact solution I was looking for - juts couldn't put it into as good technical words as you did there. Thankfully, if this for some reason DOESN'T work out, I'm only out of a cheap cable realistically. I'll post my results later on tonight!

Wooooohoo!!! You guys couldn't possibly comprehend how flipping excited and proud of myself I am right now! Granted it's  asimple opperation - strip the wires inside, strip the cable, twist em together - but it WORKS!!! After a week or so of struggling with one-sided, unreliable cardboard-box sound, my right monitor is back for round two!
 
Thanks Cactus, and of course everyone else who gave input
 
(Edit): humorously enough, it looked like my cable, which had red/white shieldings, was OPPOSITE the speaker which had red/black. I had it inititally with the reds connected and was wondering why it felt like all the bass was gone in my test tracks and that the bass would come back when everything is panned to only one side. haha!