Brown coolant even after multiple flushes?

I have a 65 F100. I've had it just over a year and have flushed the radiator several times. Each time the coolant comes out brown in color and sometimes has clumps of stuff (not sure what it is) in it. The entire rad support was full of dirt and rocks, along with the under carriage. I'm thinking the previous owner did a lot of driving around in the dirt/mud.
My question is this, how the heck do I clear this up? I'm hoping that I don't have to tear apart the block....as I don't know squat about engines yet.
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