Ajax with jQuery UI dialog not working

I am trying to update my custom database table when changes are made in a dialog box. The script for the dialog box and ajax call is as follows –

jQuery(document).ready(function($){

$("td > span").click(function(){

    var id = $(this).attr('id');
    var message = "message"+id;
    var content = jQuery("#"+message).text();
    var $dialog = $("<div></div>").html("<textarea style='width:99%; height:90%' class='popup-content'>"+content+"</textarea>").dialog({
        height: 400,
        width: 400,
        title: 'My Data',
        modal: true,
        autoOpen: false,
        dialogClass: 'wp-dialog',
        buttons: {
            "Save": function(){
                $("#"+message).html($(".popup-content").val());
                $.ajax({
                    type: "post",
                    url: "admin-ajax.php",
                    data: {
                        action: "feedmng_update",
                        feed_id: id
                    }
                });
            }
        }
    });
    $dialog.dialog("open");
  });
});

The above script works all well but for the Ajax part. The above code is a separate javascript file which I even enqueue in my php file. The following is the Ajax call related code to update database having the id passed during the Ajax call –

function __construct(){
  add_action( 'wp_ajax_feedmng_update', array( &$this, 'feedmng_update' ) );
}

function feedmng_update(){

    global $wpdb;
    $feedid = $_REQUEST["feed_id"];
    $wpdb->update( $wpdn->feedmanager, array( 'message' => "New data" ), array( 'id',$feedid ) );
}

My table name is wp_feedmanager and I am trying to update it’s ‘message’ column. But it just wont update ? Any suggestions what should be done ?