Converting/Casting List<string> to List<ulong>

Question

I've been trying to cast List<string> property to List<ulong> property. It seems no matter what I do, it keeps failing to get or set data.

public List<string> _DocumentIds { get; set; } = new List<string>();

Things I've tried to convert List<string> to List<ulong>:

Using ConvertAll

public List<ulong> DocumentIds 
{ 
  get => _DocumentIds.ConvertAll(x => UInt64.Parse(x)); 
  set => _DocumentIds = value.ConvertAll(x => $"{x}"); 
}

Using Casts

public List<ulong> DocumentIds 
{ 
   get => _DocumentIds.Cast<ulong>().ToList(); 
   set => _DocumentIds = value.Cast<string>().ToList(); 
}

Using Select

public List<ulong> DocumentIds
{
   get => _DocumentIds.Select(x => UInt64.Parse(x)).ToList();
   set => _ = value.Select(x => $"{x}").ToList();
}

Something I'm not proud of

public List<ulong> DocumentIds
{
   get
   {
      var Values = new List<ulong>();
      foreach (var Value in _DocumentIds) Values.Add(UInt64.Parse(Value));
      return Values;
   }
   set => _DocumentIds = value.Cast<string>().ToList();
}

I've used breakpoints on get set statements and it always hit get twice but never hits set.