使用AJAX修改xml

I have the following xml file:

<User>
    <Address>123</Address>
    <FirstName>John</FirstName>
    <SecondName>Smith</FirstName>
</User>

I am trying to get it changed with an AJAX call:

var addressid= = 123;
    $.ajax({
                                                    type: "GET",
                                                    url: url,
                                                    headers: {
                                                    "Authorization": "Basic " + btoa("username:password"),
                                                    },
                                                    contentType: "application/xml",
                                                    dataType: "xml",
                                                    async: true,
                                                    crossDomain: true,
                                                    success: function(xmlResponse) {
                                                    alert("Your user has been edited");
                                                    $(xmlResponse).find('User').each(function(){
                                                                                     if($(this).find('Address').text() == addressid) {
                                                                                     $(this).find('FirstName').text("Jenifer");
                                                                                     $(this).find('SecondName').text(secondName);
                                                                                     }
                                                                                     });
                                                    }
                                                    });

An alert comes, this does not display any errors, but it doesn't get passed on to the system. Which means, if I fetch the data from the server, the old name gets displayed. What am I doing wrong?