Description environment with line break and no indent in labels but indented body

I have a description list with a label that does not a fit on one line. I want a line break in the label such that the second line of the label is not indented. I still want the body text to be indented. (To get the body text to start on a new line I use the hack ~\\—perhaps there is a better solution?)

\documentclass{article}
\usepackage{enumitem}
\usepackage{lipsum}
\begin{document}
\begin{description}[style=unboxed]
\item[
This is a too long label.
It would not be if I did not add this sentence.
I do not want this line to be indented.
]~\\
However, I want the body of the item to be, just as it is.
\lipsum[1]
\item[An item with a short label.]~\\
This looks good.
\lipsum[1]
\end{description}
\end{document}


This is not right - it produces overfull boxes. However, perhaps somebody else will find it a useful basis for a better solution.

\documentclass{article}
\usepackage{enumitem,calc}
\usepackage{lipsum}
\makeatletter
\SetLabelAlign{myparleft}{\parbox[t]\textwidth{#1\par\mbox{}}}
\makeatother
\begin{document}
\lipsum[1]
\begin{description}[align=myparleft]
\item[%
This is a too long label.
It would not be if I did not add this sentence.
I do not want this line to be indented.
]
However, I want the body of the item to be, just as it is.
\lipsum[1]
\item[An item with a short label.]
This looks good.
\lipsum[1]
\end{description}
\end{document}


Building on cfr's answer, here are two solutions. However it requires manual setting the number of lines in the description.

\documentclass{article}
\usepackage{enumitem}
\usepackage{lipsum}
\begin{document}
\begin{description}[style=unboxed]
\item[\protect{%
\parbox[t][2\baselineskip][t]{\textwidth}{%
This is a too long label.
It would not be if I did not add this sentence.
I do not want this line to be indented.
}
}]
Now this looks good,
with the description wrapped in a parbox.
\lipsum[75]
\item[An item with a short label.]~\\
This looks good.
\lipsum[66]
\item[\protect{%
\begin{minipage}[t][2\baselineskip][t]{\textwidth}
This is a too long label.
It would not be if I did not add this sentence.
I do not want this line to be indented.
\end{minipage}
}]
And this looks good too,
with the description wrapped in a minipage.
\lipsum[75]
\end{description}
\end{document}