Just because I hate finding questions online with no resolution, I'm coming back with the answer. Here is how I was able to find the link I was looking for within the page's HTML:

my @test_frames = $mech->xpath('/html/body/div/p/a', one => 1, frames 
+=> 1);
printf(TEST_FH "result is %s\n", $test_frames[0]->{outerHTML});
[download]

I obtained the xpath using Firebug (highlight the link on the webpage, right click, select "copy Xpath") then used the outerHTML (as opposed to innerHTML) to get the URL.