Display multiple types from a single list in a WPF ListBox?

I have an ObservableCollection<Object> that contains two different types.

I want to bind this list to a ListBox and display different DataTemplates for each type encountered. I can't figure out how to automatically switch the data templates based on the type.

I have attempted to use the DataType property of the DataTemplate and attempted using ControlTemplates and a DataTrigger, but to no avail, either it nothing shows up, or it claims it can't find my types...

Example Attempt below:

I only have the one data template wired to the ListBox right now, but even that doesn't work.

XAML:

<Window x:Class="WpfApplication1.Window1"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
Title="Window1" Height="300" Width="300">
<Window.Resources>
    <DataTemplate x:Key="PersonTemplate">
        <TextBlock Text="{Binding Path=Name}"></TextBlock>
    </DataTemplate>

    <DataTemplate x:Key="QuantityTemplate">
        <TextBlock Text="{Binding Path=Amount}"></TextBlock>
    </DataTemplate>

</Window.Resources>
<Grid>
    <DockPanel>
        <ListBox x:Name="MyListBox" Width="250" Height="250" 
ItemsSource="{Binding Path=ListToBind}"
ItemTemplate="{StaticResource PersonTemplate}"></ListBox>
    </DockPanel>
</Grid>
</Window>

Code Behind:

public class Person
{
    public string Name { get; set; }

    public Person(string name)
    {
        Name = name;
    }
}

public class Quantity
{
    public int Amount { get; set; }

    public Quantity(int amount)
    {
        Amount = amount;
    }
}

public partial class Window1 : Window
{
    ObservableCollection<object> ListToBind = new ObservableCollection<object>();

    public Window1()
    {
        InitializeComponent();

        ListT