My hood release cable broke off, on my 2001 Corolla.

I intend to jack the car up high and put it on jack stands so I will have some room to get under the rad to get access.  I am a 6ft 250 pound male, so my arms are not skinny or super flexible.  Think forearms like Popeye.  I have a lot of hand tools, including boxend metric wrenchs that click like a socket in as little as 5 degrees.  This is what I think will with some sort of extension handle allow me to unbolt the entire latch assembly.

     This will likely be a slow and frustrating process, there has got to be a better way, so handy people show me a better way.  Thanks in advance Phil aka zipperboy, adventureboy7 etc.

I feel your pain, I hate working on small cramped cars. Here's an idea to think about. depending on the type of latch can you loop a piece of cord around the latch and pull it to open the catch. Or can you find where the cable broke (you didn't say how close to the latch it broke) and grab the remaining cable and pull it to open. Sometimes it's the simple stuff we overlook that kicks you in the butt. Once you get it open make sure not to accidentally close it again, Murphys Law and working on cars goes hand in hand!