Well, it's possible to achieve that though either AngularJS or Laravel or http server side, but it's better & easier to be done through Laravel itself since we can just override the required classes (URLGenerator mainly) without touching core files, and while keeping the code (server agnostic), so it could work with apache/nginx or any other server with trailing slash (that's why I preferred not to work with htaccess).
Update #1
Laravel 5 / AppServiceProvider::register()
$this->app->bindShared('url', function ($app) {
$routes = $app['router']->getRoutes();
$request = $app->rebinding('request', function ($app, $request) {
$app['url']->setRequest($request);
});
// This is your custom overridden "UrlGenerator" class
$urlGenerator = new UrlGenerator($routes, $request);
return $urlGenerator;
});