Automatic conversion of your curl command line to Perl using HTTP::Request::FromCurl (via curl-to-lwp gives the following:

#!perl
use strict;
use warnings;
use WWW::Mechanize;
use HTTP::Request;


my $ua = WWW::Mechanize->new();
my $r  = HTTP::Request->new(
    'POST' => 'https://api.blockchain.info/v2/receive/balance_update',
    [
        'Accept'         => '*/*',
        'Host'           => 'api.blockchain.info:443',
        'User-Agent'     => 'curl/7.55.1',
        'Content-Length' => '169',
        'Content-Type'   => 'text/plain',
    ],
'{"key":"[your-key-here]","addr":"183qrMGHzMstARRh2rVoRepAd919sGgMHb",
+"callback":"https://mystore.com?invoice_id=123","onNotification":"KEE
+P", "op":"RECEIVE", "confs": 5}'
);
my $res = $ua->request( $r, );


__END__

Created from curl command line

curl -H "Content-Type: text/plain" --data '{"key":"[your-key-here]","a
+ddr":"183qrMGHzMstARRh2rVoRepAd919sGgMHb","callback":"https://mystore
+.com?invoice_id=123","onNotification":"KEEP", "op":"RECEIVE", "confs"
+: 5}' https://api.blockchain.info/v2/receive/balance_update
[download]

You'll note how the request is different from your setup of the request. Most of that is likely due to not duplicating the parameters faithfully.