Can't change state of checkable QListViewItem with custom widget

I have a QListWidget where I want to add a bunch of items with a custom widget:

Code:

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#include <QApplication>
#include <QListWidget>
#include <QListWidgetItem>
#include <QPushButton>
 
int main(int argc, char** argv)
{
	QApplication* app = new QApplication(argc, argv);
	QListWidget* listWidget = new QListWidget();
	QListWidgetItem* item = new QListWidgetItem();
	item->setFlags(item->flags() | Qt::ItemIsUserCheckable);
	item->setCheckState(Qt::Unchecked);
	listWidget->addItem(item);
	QWidget* widget = new QPushButton("Example widget");
	item->setSizeHint(widget->sizeHint());
	listWidget->setItemWidget(item, widget);
 
	listWidget->show();
	app->exec();
}

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The problem is that I can not use the checkbox that appears in the listwidget next to the added widget. It looks completely normal, but nothing happens when I click on it. If I remove the line with setSizeHint it works correctly, but then my widget is no longer visible. How do I solve this problem?