The short answer: revelation to Joseph Smith.
The long answer:
The LDS edition of the King James Version (KJV plus references) was authored in 1979 under the direction of the Apostles:
In 1979 and 1981, following a historic effort led by Elders Thomas S. Monson, Boyd K. Packer, and Bruce R. McConkie of the Quorum of the Twelve Apostles, The Church of Jesus Christ of Latter-day Saints published its own edition of the King James Version of the Bible.
This edition includes footnotes with excepts from the Joseph Smith Translation (selected Biblical translations by Joseph Smith circa 1830).
But I speak unto you who are called unto the ministry. For this I say, brethren, the time that remaineth is but short, that ye shall be sent forth unto the ministry. Even they who have wives, shall be as though they had none; for ye are called and chosen to do the Lord’s work.
JST, 1 Corinthians 7:29
For comparison, the plain KJV:
But this I say, brethren, the time is short: it remaineth, that both they that have wives be as though they had none;
KJV, 1 Corinthians 7:29
Note the JST was an inspired rather than conventional translation; there's no claim that extant Greek texts have this content.
The Lord inspired the Prophet Joseph Smith to restore truths to the King James Bible text that had become lost or changed since the original words were written. These restored truths clarified doctrine and improved scriptural understanding.
Because the Lord revealed to Joseph certain truths that the original authors had once recorded...the word translation is used in a broader and different way than usual, for Joseph’s translation was more revelation than literal translation from one language into another.
This interpretation is doctrinally consistent with the otherwise pro-marriage instructions throughout the scriptures. (Genesis 1, Matthew 19, even Paul himself in 1 Timothy 4:3.)
The Church of Jesus Christ of Latter-day Saints follows Paul's instruction, in that the vast majority of its full-time missionaries are required to be single. As Paul said, those responsibilities are incompatible with marriage. (But following that full-time service they would marry and raise children.)