HashSet that preserves ordering

Standard .NET HashSet do not preserve the insertion order.
For simple tests the insertion order may be preserved due to an accident, but it’s not guaranteed and would not always work that way. To prove that it is enough to do some removals in between.

See this question for more information on that: Does HashSet preserve insertion order?

I have briefly implemented a HashSet which guarantees insertion order. It uses the Dictionary to look up items and the LinkedList to preserve order. All three insertion, removal and lookup work still in O(1).

public class OrderedSet<T> : ICollection<T>
{
    private readonly IDictionary<T, LinkedListNode<T>> m_Dictionary;
    private readonly LinkedList<T> m_LinkedList;

    public OrderedSet()
        : this(EqualityComparer<T>.Default)
    {
    }

    public OrderedSet(IEqualityComparer<T> comparer)
    {
        m_Dictionary = new Dictionary<T, LinkedListNode<T>>(comparer);
        m_LinkedList = new LinkedList<T>();
    }

    public int Count => m_Dictionary.Count;

    public virtual bool IsReadOnly => m_Dictionary.IsReadOnly;

    void ICollection<T>.Add(T item)
    {
        Add(item);
    }

    public bool Add(T item)
    {
        if (m_Dictionary.ContainsKey(item)) return false;
        var node = m_LinkedList.AddLast(item);
        m_Dictionary.Add(item, node);
        return true;
    }

    public void Clear()
    {
        m_LinkedList.Clear();
        m_Dictionary.Clear();
    }

    public bool Remove(T item)
    {
        if (item == null) return false;
        var found = m_Dictionary.TryGetValue(item, out var node);
        if (!found) return false;
        m_Dictionary.Remove(item);
        m_LinkedList.Remove(node);
        return true;
    }

    public IEnumerator<T> GetEnumerator()
    {
        return m_LinkedList.GetEnumerator();
    }

    IEnumerator IEnumerable.GetEnumerator()
    {
        return GetEnumerator();
    }

    public bool Contains(T item)
    {
        return item != null && m_Dictionary.ContainsKey(item);
    }

    public void CopyTo(T[] array, int arrayIndex)
    {
        m_LinkedList.CopyTo(array, arrayIndex);
    }
}