Change Quick Launch Flyout width without changing Top Navigation

We are using SharePoint 2013 and just enabled the ability to have fly out menus on our Quick Launch. We need to increase the width of the menu items though, so we found this code to do that.

<style>
     .menu-item
     {
         background-color:white;
         width:175px;
     }</style>

The problem is that this also changes the width of the menu items in the top navigation bar, which we don't want it to do. Is there a way to change the width of the fly out menus without changing the width of the top navigation items?

Though I didn't try it, I would assume changing the background or hover color would also change it for the top nav, too. Is there a way to do that as well?

Thank you!