Unless I am not fully awake yet, it appears that you are using backtics "`" as opposed to single quotes "'" to assign a value:

my $cmd = `ls -l`;
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The end effect of this is that you are telling perl to execute the command inside the backtics, and place any output from STDOUT in the variable $cmd. I presume that what you want is to assign the string consisting of 'ls -l' to $cmd which is then executed on the remote host.

EDIT: Simplistic demo of above:

$ cat backtictest.pl 
#!/usr/bin/perl

use strict;
use warnings;

my $cmd_sq = 'ls -l';
print "Using single quotes: $cmd_sq\n\n";

my $cmd_bt = `ls -l`;
print "Using backtics: $cmd_bt\n";

exit;

__END__

Output:
Macintosh-45:stuff user$ ./backtictest.pl 
Using single quotes: ls -l

Using backtics:
-rw-r--r--  1 user  group    260 May  6 17:58 Class1.pm
-rw-r--r--  1 user  group    260 May  6 17:58 Class2.pm
-rw-r--r--  1 user  group    331 May  6 17:58 MyExceptions.pm
-rwx------  1 user  group    182 May 21 07:38 backtictest.pl
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