My water line broke, after the fix, I ran a tub to clean out the line,
but forgot that we had flushed the toilet, so it began to fill with the
dirty water as soon as water was turned back on.

Now there is dirt/stone or something blocking the intake to my toilet.
A small amount of water comes through, but takes about 30 minutes to
fill. The overflow water pressure line is fine.

How can I take this apart to clean it out? There aren't any screws at
the top of the assembly.
It appears to be one piece. Does it screw off? Snap off? how can I
take the whole assembly out of the tank if needed?

(I'm not very skilled, but willing to try, to avoid the hassle,
expense, of trying to find a plumber on the Thanksgiving holiday
weekend, plus I work full-time, so can't be home during the week)