Here is the text of the Kol Nidre prayer, as given in the book "Gates of Repentance: The New Union Prayerbook for the Days of Awe" published in 1978 by the Central Conference of American Rabbis:

"Let all our vows and oaths, all the promises we make and the obligations we incur to You, O God, between this Yom Kippur and the next, be null and void should we, after honest effort, find ourselves unable to fulfill them. Then may we be absolved of them."

The key phrase to make note of here is "to You, O God". The subject of this prayer is promises made TO GOD, not promises made TO OTHER PEOPLE. In order to emphasize this point, the following passage is included in the prayerbook immediately prior to Kol Nidre:

"For transgressions against God, the Day of Atonement atones; but for transgressions of one human being against another, the Day of Atonement does not atone until they have made peace with one another."

Also, note the requirement for "honest effort" to comply in the case of promises made to God.

[For those who may not be familiar with the terms, the Day of Atonement, known as Yom Kippur in Hebrew, is the 10th day of the Jewish year, and generally falls somrtime in September. It is observed with a 24-hour fast and prayers for forgiveness of sin. Like all Jewish holidays, it begins on sundown of the preceding day and ends at sundown as well. The Kol Nidre prayer is recited at the evening service at the start of Yom Kippur. In Biblical times, the month which is now the first month (known by the Babylonian-origin name of Tishri) was considered the 7th month, since the year then began in spring. The Book of Exodus (or possibly Leviticus) describes the original procedures for observing the Day of Atonement on the 10th day of the 7th month. The 10-day period beginning with the Jewish New Year (Rosh Hashonah or "Head of the Year") and ending with Yom Kippur is known as the Days of Awe or the High Holy Days.]