How to clean really dirty grout on a tile floor?

I'm going to be moving into a new house relatively soon & I'm having a huge issue with the grout in the bathroom tile floor. At first I thought it was just stained, but after a ridiculous number of floor washings I noticed that there is actually something packed into the grout spaces. There's quite a bit of "dirt" packed in every single space. Washing & scrubbing is just not enough. I can get the top of the tile sparkly clean, but it takes forever to scrub the dirt out of the gaps. Re-doing the floor is not an option. Any suggestions on how to loosen the stuff stuck in the grout?