Allow saving an existing entry in Laravel with FormRequest and unique

Still noob and learning Laravel, I am currently in the middle of a simple validation with FormRequest. What I am facing today is the edit of an existing entry. I have written in my FormRequest that I want the name to be unique. I works perfectly but of course when I edit an existing entry, I cannot save it anymore, it already exists... of course it does since I am editing it. Anyway, I found the solution reading the documentation, but unfortunately, it does not work. Here's my code:

Routes:

Route::resource('editeurs', 'PublishersController');

Controller:

class PublishersController extends Controller
{
    /* Update an existing publisher */
    public function update($slug, PublisherRequest $request)
    {
        $publisher = Publisher::where('slug', $slug)->firstOrFail();

        $input = $request->all();

        $publisher->name = $input['name'];
        $publisher->slug = my_slug($input['name']);

        $publisher->update();

        return redirect()->action('PublishersController@show', $publisher->slug);
    }
}

FormRequest:

class PublisherRequest extends Request
{
    /**
     * Get the validation rules that apply to the request.
     *
     * @return array
     */
    public function rules()
    {
        return [
            'name' => 'required|unique:publishers,name,'.$this->get('id')
        ];
    }
}

If needed, the view: @section('content') Edition - {!! $publisher->name !!}

        {!! Form::model($publisher, ['method' => 'PATCH', 'action' => ['PublishersController@update', $publisher->slug]]) !!}
        <div class="large-12 columns">
            {!! Form::label('name', 'Nom de l\'éditeur') !!}
            {!! Form::text('name', null, ['placeholder' => 'Nom de l\'éditeur']) !!}
        </div>

        <div class="large-12 columns">
            {!! Form::submit('Ajouter un éditeur', ['class' => 'button expand']) !!}
        </div>
        {!! Form::close() !!}
    </div>
@stop

What is wrong with my code?

via Chebli Mohamed