You have a record separator: "address", it's just disguised as a record heading. Perl knows how to deal with alternate record separators (alternate to "\n", that is), as long as they can be represented as a literal string.

local $/ = q{address};    # Set record separator to 'address'.
open my $infile, '<', 'filename.txt' or die $!;
print "This is the list of addresses\n",
      "here are the addresses\n";
while( <$infile> ) {
    chomp;                # chomp removes the trailing record separato
+r.
    s/^\s+|\s+$//g;
    next unless length;
    print "address $_\n";
}
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