Replacing American Standard flush valve/ballcock combo ?

Hello all -
Apologies ahead of time if I end up asking the the stupidest questions you plumbers out there have ever heard, but I'm stuck. I'm trying to replace a leaking flush valve in my American Standard one-piece gravity flush (I assume) toliet. There's a constant leak running into the bowl, and my water bill is starting to show it. It's not the flapper, because I can hear the water running until I lift the ballcock arm high enough for it to stop. When I do that, the water stops running into the bowl as well. So here's my real problem. I've replaced valve/ballcock on toilets in my previous house with the Fluidmaster 10$ combos from Home Depot. This one's unlike anything I've ever seen, and I want to be sure of what I'm doing. Instead of a flush valve and refill tube being separate, this toliet has what looks like the refill tube directly attached to the flush valve, screwed into the flush valve at the top. There's a hose at the top of the refill tube that runs into a side corner of the tank that I'm assuming is the feed for the top of the bowl when you flush. Do I have to replace this with American Standard replacement parts? I went to the website, but that didn't get me anywhere (mostly sales stuff). Is is safe (or even possible) to replace the AS setup with the regular Fluidmaster and just run the feed tube into the side corner of the tank? I'm assuming not. The toilet itself has 680 2007 stamped on the inside of the tank. It also says 4192 - Apr 14 stamped into it as well. Any help/insight greatly appreciated.
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JavaMan wrote:

Terminology: Flush valve is the part which has the flapper (or disc float) and lets water into the bowl from the tank. Ballcock is the part which lets supply water fill the tank until the float arm rises.
You may be better off rebuilding the old ballcock. It should have a replaceable rubber washer (the washer is similar to a faucet washer but different size). If a Fluid Master ballcock will fit the tank height, you can use it and route the plastic refill tube into the cavity at the corner of the tank. You *do* have to be certain the end of the tube is kept *above* the rim of the cavity or self-siphoning can occur.
Jim
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Are you sure you don't have it adjusted so that the tank water level is set to be higher than the top of the overflow tube? If you have that, it will.....overflow.

. There's a constant leak

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