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Number theory Difficulty 3.0 AMC 10/12 Find the answer Canada

Two 3-digit integers, $abc$ and $def$ , have the following property:

$\begin{array}{r} a\ b\ c \\ +\ d\ e\ f \\ \hline 1\ 0\ 0\ 0 \end{array}$

None of $a, b, c, d, e,$ or $f$ is $0$ . What is $a+b+c+d+e+f$ ?

(A) $10$ (B) $19$ (C) $21$ (D) $28$ (E) $30$

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.