$req->header('Accept' => 'application/xml');
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I gave that a try and it still didn't work.. I got the same error message: "The server refused this request because the request entity is in a format not supported by the requested resource for the requested method."

I think perhaps there was a confluence of almost right in the advice, try this mix (default auth headers like I showed before are more convenient because you only do it once)–

use strict;   # Never-
use warnings; # -skip these.
use LWP::UserAgent;

my $urlRequest = "http://bamboohost/rest/api/latest/result/projectname
+-planname-latest/label";

my $xml = <<'';
<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
<label name="testlabel"/>

my $ua = LWP::UserAgent->new;
my $post = HTTP::Request->new( POST => $urlRequest );
$post->authorization_basic("username", "password");
$post->content($xml);
$post->content_type("application/xml");
print $post->as_string;

my $result = $ua->request( $post );
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