如何从jQuery ajax调用gatewayapi？

I am using gatewayapi.com to send sms from a php script. It works great. But when I try to call the same script from jQuery ajax it will not work. Can someone please tell me how to do it? This is my php code that works.

$recipients = ['myphonenumber'];
$url = "https://gatewayapi.com/rest/mtsms";
$api_token = "mytoken";
$json = [
    'sender' => 'mysender',
    'message' => 'mymessage',
    'recipients' => [],
];
foreach ($recipients as $msisdn) {
    $json['recipients'][] = ['msisdn' => $msisdn];
}

$ch = curl_init();
curl_setopt($ch,CURLOPT_URL, $url);
curl_setopt($ch,CURLOPT_HTTPHEADER, array("Content-Type: application/json"));
curl_setopt($ch,CURLOPT_USERPWD, $api_token.":");
curl_setopt($ch,CURLOPT_POSTFIELDS, json_encode($json));
curl_setopt($ch,CURLOPT_RETURNTRANSFER, true);
$result = curl_exec($ch);
curl_close($ch);

This is my javascript that do not work.

<script>
function send_sms() {
    $.ajax({
    dataType: "json",           
    type: "POST",
    async: false,
    url: 'sendsms.php',
    data: {
    message: 'mymessage'
    },
    cache: false,           
    success: function(data)
        {

        }             
    });
}
</script>

I also tried to call the php script from a cronjob but that do not work.