How to link a Custom Post Type submenu to a Nextgen Gallery page?

I’ve created a custom posts top level menu item but I would like to have a submenu under that linking to the Add Gallery page of Nextgen, as the client wants all their functionality bundled up under one top level menu item.

So far I’m doing :

add_submenu_page( 
    'edit.php?post_type=events', 
    'Add Gallery', 
    'Add Gallery', 
    'administrator', 
    'nggallery-add-gallery', 
    'event_add_gallery'
);

But the link looks like:

http://example.com/wp-admin/edit.php?post_type=events&page=nggallery-add-gallery

Is there any way to achieve this?

It would go like this (note the absence of the function parameter – and also the capability instead of a role).

add_action( 'admin_menu', 'wpse_74421_menu_admin' );

function wpse_74421_menu_admin() 
{
    add_submenu_page( 
        'edit.php?post_type=events', 
        'Add Gallery', 
        'Add Gallery', 
        'delete_plugins', 
        'admin.php?page=nggallery-add-gallery'
    );
}