Remove woocommerce shipping labels from cart and checkout

I do not want the label ‘Shipping: Free Shipping’ to be shown on Cart and Checkout. Tried using the following snippet, but it didn’t work.

add_filter( 'woocommerce_cart_shipping_method_full_label', 'remove_shipping_label', 10, 2 );

function remove_shipping_label( $label, $method ) {
	$new_label = preg_replace( '/^.+:/', '', $label );

	return $new_label;

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